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Kawa: Compiling Scheme to Java

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1.4 Numbers

Scheme defines a "numerical tower" of numerical types: number, complex, real, rational, and integer. Kawa implements the full "tower" of Scheme number types, which are all sub-classes of the abstract class Quantity discussed in 1.6 Quantities.

class Complex extends Quantity {
  public abstract RealNum re ();
  public abstract RealNum im ();

Complex is the class of abstract complex numbers. It has three subclasses: the abstract class RealNum of real numbers; the general class CComplex where the components are arbitrary RealNum fields; and the optimized DComplex where the components are represented by double fields.

class RealNum extends Complex {
  public final RealNum re ()
  { return this; }
  public final RealNum im ()
  { return IntNum.zero(); }
  public abstract boolean isNegative ();

class DFloNum extends RealNum {
  double value;

Concrete class for double-precision (64-bit) floating-point real numbers.

class RatNum extends RealNum {
  public abstract IntNum numerator();
  public abstract IntNum denominator();

RatNum, the abstract class for exact rational numbers, has two sub-classes: IntFraction and IntNum.

class IntFraction extends RatNum {
  IntNum num;
  IntNum den;

The IntFraction class implements fractions in the obvious way. Exact real infinities are identified with the fractions 1/0 and -1/0.

class IntNum extends RatNum {
  int ival;
  int[] words;

The IntNum concrete class implements infinite-precision integers. The value is stored in the first ival elements of words, in 2's complement form (with the low-order bits in word[0]).

There are already many bignum packages, including a couple written in Java. What are the advantages of this one?

If the integer value fits within a signed 32-bit int, then it is stored in ival and words is null. This avoids the need for extra memory allocation for the words array, and also allows us to special-case the common case.

As a further optimization, the integers in the range -100 to 1024 are pre-allocated.

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